proposed

approved

editing

proposed

allocated for Paul DE.g.f. B(x) = B(x,x), where B(x,y) is the e.g.f. of triangle A326798. Hanna

1, -1, 1, 119, -671, -118801, 1578721, 472546983, -11434861759, -5281001286433, 202651641610561, 134214161576815319, -7489030360212947039, -6743315366908570697521, 515685193530081985152289, 606502419281376583942534919, -60891202949811176406832459647, -90683512562992732210541162641985, 11568533431831545319762169579235457, 21284623320002783970199662076124812599

0,4

Equals the row sums of triangle A326798.

E.g.f. B(x) and related functions A(x) and C(x), defined by A326794 and A326796, respectively, satisfy:

(1) A(x)^2 + B(x)^2 + C(x)^2 = 1,

(2) A(x)*A'(x) + B(x)*B'(x) + C(x)*C'(x) = 0.

E.g.f.: B(x) = 1 - x^2/2! + x^4/4! + 119*x^6/6! - 671*x^8/8! - 118801*x^10/10! + 1578721*x^12/12! + 472546983*x^14/14! - 11434861759*x^16/16! - 5281001286433*x^18/18! + 202651641610561*x^20/20! + ....

(PARI) {a(n) = my(Ax=x, Bx=1, Cx=x, Ay=y, By=y, Cy=1);

for(i=0, 2*n+1,

Ax = 0 + intformal( Bx*Cy - Cx*By, x) + O(x^(2*n+2));

Bx = 1 + intformal( Cx*Ay - Ax*Cy, x) + O(x^(2*n+2));

Cx = 0 + intformal( Ax*By - Bx*Ay, x) + O(x^(2*n+2));

Ay = 0 + intformal( By*Cx - Cy*Bx, y) + O(y^(2*n+2));

By = 0 + intformal( Cy*Ax - Ay*Cx, y) + O(y^(2*n+2));

Cy = 1 + intformal( Ay*Bx - By*Ax, y) + O(y^(2*n+2));

);

sum(k=0, n\2, (2*n)! * polcoeff( polcoeff(Bx, 2*n-2*k, x), 2*k, y))}

for(n=0, 20, print1( a(n), ", "))

Cf. A326794, A326796, A326798.

allocated

sign

Paul D. Hanna, Aug 05 2019

approved

editing

allocated for Paul D. Hanna

allocated

approved